We derive explicit expressions for the three 2 × 2 generalized Barnett-Lothe tensors S, H and L associated with the anti-plane deformations of monoclinic piezoelectric materials with symmetry plane at x₃ = 0 and with poling in the x₃-direction. The resulting generalized Barnett-Lothe tensors contain four independent components which are, in turn, expressed explicitly in terms of the ten electroelastic constants as well as the sum and product of the two Stroh eigenvalues. Concise and elegant expressions are obtained for the generalized Barnett-Lothe tensors for orthotropic piezoelectric materials.

中文翻译：

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单斜压电材料反平面变形的广义 Barnett-Lothe 张量

我们推导出三个 2 × 2 广义 Barnett-Lothe 张量S、H和L 的显式表达式，这些张量与具有x ₃  = 0处的对称平面且在x ₃方向极化的单斜压电材料的反平面变形相关。得到的广义 Barnett-Lothe 张量包含四个独立的分量，这些分量依次用十个电弹性常数以及两个 Stroh 特征值的总和和乘积明确表示。对于正交各向异性压电材料的广义 Barnett-Lothe 张量，获得了简洁而优雅的表达式。